Re: RIF RDF and OWL compatibility - mini review

>>> I don't see how the fix up of constraining the truth valuation so 
>>> that the frame and non-frame representations are equivalent works. In 
>>> BLD predicates and constants are required to be disjoint so I don't 
>>> see how the constraints like:
>>>   It-dl( t [ rdf:type -> A] ) = IR(A)(t)
>>> can be applied.
>>
>> These are not constraints, but definitions.  Effectively, they make 
>> frames just another way of writing unary and binary predicates.
> 
> Yes though with the well-formedness restrictions in BLD you can only 
> write them one way or the other, you can't mix and match, right?

Correct. As far as the BLD syntax is concerned, they are terms.

> 
>>> Either this is a pure syntactic preprocessing step (in which case 
>>> case define it as such, instead of via semantic fix up) or you are 
>>> lifting that restriction in the BLD semantics.
>>
>> It could have been defined as a syntactic preprocessing step 
>> (rewriting frames to unary and binary predicates); this is explained 
>> just above section 4.3.2.1.  However, I find the current definition 
>> more elegant, because it provides a direct semantics, rather than 
>> requiring two steps (rewriting and interpretation).
> 
> A plausible argument, I'll have to let it sink in.
> 
>>> In that case why not use that for RDF and OWL FULL as well?
>>
>> It would disallow quantification over classes and properties, i.e., no 
>> variables are allowed to occur in class or property positions. I 
>> believe that such a restriction is unacceptable for RDF-rules.  Plus, 
>> it is unclear to me what the consequences would be of using equality 
>> in the rules in such a setting.
> 
> I was thinking that you must have lifted the disjointness constraints on 
> BLD in which case one could write in frame form when you want such 
> quantification and in predicate form when you didn't.

We did think about this.  However, we did not see a way to tie the 
semantics of such frames and such predicates together in a satisfactory 
way.
For example, it is possible to define the semantics of combinations 
based on frames, and add the following axiom schemas:
C(x) :- x[rdf:type -> C] and R(x, y) :- x[R -> y]

However, statements made about the predicates are then not subject to 
the semantics of the ontology.
Consider, for example, an RDFS ontology with the statement: C subClassOf D
and a rule set with the single fact C(a)

the combination of the ontology and the rule set with the mentioned 
axiom schemas does not entail D(a).  However, a combination of the 
mentioned ontology with a rule set comprising the fact a[rdf:type -> C] 
does entail a[rdf:type -> D]


Best, Jos

> Without lifting 
> those restrictions I can see that you can only write in one form or the 
> other in which case you are are right, the predicate form *on its own* 
> is not sufficient for RDF.
> 
> Dave

-- 
                          debruijn@inf.unibz.it

Jos de Bruijn,        http://www.debruijn.net/
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